Refined estimates and generalization of some recent results with applications

Aqeel Ahmad Mughal; Deeba Afzal; Thabet Abdeljawad; Aiman Mukheimer; Imran Abbas Baloch; Aqeel Ahmad Mughal; Deeba Afzal; Thabet Abdeljawad; Aiman Mukheimer; Imran Abbas Baloch

doi:10.3934/math.2021623

AIMS Mathematics

2021, Volume 6, Issue 10: 10728-10741. doi: 10.3934/math.2021623

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Research article

Refined estimates and generalization of some recent results with applications

1.
Department of Mathematics and Statistics University of Lahore, Lahore, Pakistan
2.
Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan
5.
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
6.
Higher Education Department, Govt. Graduate College for Boys Gulberg Lahore, Punjab, Pakistan

Received: 31 May 2021 Accepted: 06 July 2021 Published: 23 July 2021
MSC : 26A15, 26A51, 26D10, 26D15

In this paper, we firstly give improvement of Hermite-Hadamard type and Fej$ \acute{e} $r type inequalities. Next, we extend Hermite-Hadamard type and Fej$ \acute{e} $r types inequalities to a new class of functions. Further, we give bounds for newly defined class of functions and finally presents refined estimates of some already proved results. Furthermore, we obtain some new discrete inequalities for univariate harmonic convex functions on linear spaces related to a variant most recently presented by Baloch et al. of Jensen-type result that was established by S. S. Dragomir.
Citation: Aqeel Ahmad Mughal, Deeba Afzal, Thabet Abdeljawad, Aiman Mukheimer, Imran Abbas Baloch. Refined estimates and generalization of some recent results with applications[J]. AIMS Mathematics, 2021, 6(10): 10728-10741. doi: 10.3934/math.2021623

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Abstract

In this paper, we firstly give improvement of Hermite-Hadamard type and Fej$ \acute{e} $r type inequalities. Next, we extend Hermite-Hadamard type and Fej$ \acute{e} $r types inequalities to a new class of functions. Further, we give bounds for newly defined class of functions and finally presents refined estimates of some already proved results. Furthermore, we obtain some new discrete inequalities for univariate harmonic convex functions on linear spaces related to a variant most recently presented by Baloch et al. of Jensen-type result that was established by S. S. Dragomir.

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